paddy.Default_Numerics module

The paddy.Default_Numerics module contains functions for numeric problems.

Routine listings

eval_numeric(object)

polynomial(object)

poly(x,seed)

trig_inter(x,seed)

mse_func(target, output)

gramacy_lee()

Notes

The background information regarding how general functions and classes used to initiate an instance of PFARunner that are also provided as builtins in the Default_Numerics module is described in the Paddy_Runner module.

Examples

class paddy.Default_Numerics.EvalNumeric(error_func=<function mse_func>, t_func=<function gramacy_lee>, f_func=<function trig_inter>)[source]

Bases: object

Return error after evaluating a numeric function.

This class can be used to evaluate an optimization problem where fiting to a numeric value is the goal. This can range from interpolation to min-max optimization.

Parameters
seedarray-like, shape = (parameters,2)

A numpy array of parameters generated by paddy. Refer to Paddy_runner for details regarding generation of the array.

error_funcfunction, optional (default

An error function thats output is minimized by paddy. If user defined , make sure to note the internal sign change used to maximize the negative error value returned by eval_numeric.

t_funcfunction, optional (default

A target function that provides the input and target value(s) for the error and fitting functions.

f_funcfunction, optional (default

A fitting function that recieves an input generated by the target function, and returns an output to compate with the desired answer being optimized twards.

Returns
errorfloat

A numeric value that serves as the fitness value for the seed evaluated. This is defined as the negative output of the error function.

See also

mse_func()
gramacy_lee()
trig_inter()

Notes

The default functionalities of this function is evaluation of seed values as the coeficents of a trigonometric polynomial used to interpolate the Gramacy and Lee function, where the evaluation metric function is the mean squared error of the x-y coordinates of Gramacy and Lee and the generated polynomial where \(x\in[ -0.5,2.5 ]\) with a resolution of 0.001. The default and user defined instances of this class use the method eval(seed) to evaluate and return results.

Methods

eval(self, seed)

Method of eval_numeric.
eval(self, seed)[source]

Method of eval_numeric.

class paddy.Default_Numerics.Polynomial(length, scope, gausian_type, normalization=True, limits=True)[source]

Bases: object

Generate paddy space that is apt for polynomial fitting.

See also

eval_numeric
paddy.Paddy_Parameter.PaddyParameter
paddy.Default_Numerics.gramacy_lee()[source]

Return Gramacy and Lee function coordinates.

This function generates the x-y coordinates used to evaluate interpolation of the Gramacy and Lee function via a default or user defined intrerpolation function.

See also

eval_numeric()

References

1

Gramacy, R. B., & Lee, H. K. (2012). Cases for the nugget in modeling computer experiments. Statistics and Computing, 22(3), 713-722 .

paddy.Default_Numerics.mse_func(target, mse_input)[source]

Return error of interpolation.

This function returns eval_numeric()the mean squared error for two sequences of numeric values.

paddy.Default_Numerics.poly(x_list, seed)[source]

Return cordinates of a polynomial.

This function returns the 2-D cordinates of a polynomial, and is used for interpolation problems.

Parameters
x_listlist

A list of numerics that defines the x values evaluated over.

seedarray-like, shape = (parameters, 2)

A numpy array of parameters generated by paddy. Refer to Paddy_runner for details regarding generation of the array.

Returns
outputlist of floats

A list of float values representing the y values of the input x.

See also

eval_numeric()

Notes

The polynomial is defined as:

\[\sum_{k=0}^{n}a_{k}x^k\]

Where a represents the sequence of parameter values generated by paddy. x is simply the x parameter of numeric values that the polynomial is evaluated over.

paddy.Default_Numerics.trig_inter(x_list, seed)[source]

Return cordinates of a trigonometric polynomial.

This function returns the 2-D cordinates of a trigonometric polynomial, and is used for interpolation problems.

Parameters
x_listlist

A list of numerics that defines the x values evaluated over.

seedarray-like, shape = (parameters,2)

A numpy array of parameters generated by paddy. Refer to Paddy_runner for details regarding generation of the array.

See also

eval_numeric()

Notes

The trigonometric polynomial is defined as:

\[t(x)=a_{0}+\sum_{n=1}^{N}a_{n}\cos(nx)+\sum_{n=1}^{N}b_{n}\sin( nx)\]

Where a represents the sequence of parameter values generated by paddy and are passed as the odd indices of seed and b being even. Notice that this would mean that a trigonometric polynomial of the 10th degree would be defined by a paddy space of 11 individual parameters.